Pregunta
F)) Factor completely. \( 3 s^{2}+8 s-3 \) Submit
Ask by Erickson Bates. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
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The expression \(3s^{2}+8s-3\) factors to \((s+3)(3s-1)\).
Solución
Factor the expression \( 3s^2+8s-3 \).
Factor the expression by following steps:
- step0: Factor:
\(3s^{2}+8s-3\)
- step1: Rewrite the expression:
\(3s^{2}+\left(-1+9\right)s-3\)
- step2: Calculate:
\(3s^{2}-s+9s-3\)
- step3: Rewrite the expression:
\(s\times 3s-s+3\times 3s-3\)
- step4: Factor the expression:
\(s\left(3s-1\right)+3\left(3s-1\right)\)
- step5: Factor the expression:
\(\left(s+3\right)\left(3s-1\right)\)
The factored form of the expression \(3s^{2}+8s-3\) is \((s+3)(3s-1)\).
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Simplifique esta solución Beyond the Answer
To factor the quadratic expression \(3s^2 + 8s - 3\), you can look for two numbers that multiply to the product of the coefficient of \(s^2\) (which is \(3\)) and the constant term (which is \(-3\)), giving you \(-9\) (i.e., \(3 \times -3\)), while also adding up to the middle coefficient, which is \(8\). These two numbers are \(9\) and \(-1\). So, you rewrite the expression as: \(3s^2 + 9s - s - 3\) Now, group the terms: \((3s^2 + 9s) + (-s - 3)\) Factoring out the common factors gives you: \(3s(s + 3) - 1(s + 3)\) Therefore, you can factor it completely as: \((3s - 1)(s + 3)\). Happy factoring!
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